About Me

I am an Assistant Professor in the Department of Mathematical Sciences at the University of Cincinnati since Fall 2019. Previously, I was a postdoc at the University of Michigan, where my research mentor was Peter D. Miller. My PhD thesis advisor was Irina Nenciu and my thesis was on Hamiltonian perturbations of the doubly-infinite Toda lattice.

Interests
  • Nonlinear Waves
  • Integrable Systems
  • Riemann-Hilbert Problems
  • Dispersive PDEs
Education

  • PhD in Mathematics, 2015

    University of Illinois at Chicago

  • BSci & MSci in Mathematics, 2009

    Bogazici University

New Paper!

Computation of large-genus solutions of the Korteweg-de Vries equation
We consider the numerical computation of finite-genus solutions of the Korteweg-de Vries equation when the genus is large. Our method …
Deniz Bilman, Patrik Nabelek, Thomas Trogdon
April, 2022 submitted for publication
Code ArXiv
Computation of large-genus solutions of the Korteweg-de Vries equation

Publications

Computation of large-genus solutions of the Korteweg-de Vries equation
We consider the numerical computation of finite-genus solutions of the Korteweg-de Vries equation when the genus is large. Our method …
Deniz Bilman, Patrik Nabelek, Thomas Trogdon
April, 2022 submitted for publication
Code ArXiv
Computation of large-genus solutions of the Korteweg-de Vries equation
Extreme superposition: High-order fundamental rogue waves in the far-field regime
We study fundamental rogue-wave solutions of the focusing nonlinear Schrödinger equation in the limit that the order of the rogue wave …
Deniz Bilman, Peter D. Miller
April, 2022 in press, Memoirs AMS
ArXiv
Extreme superposition: High-order fundamental rogue waves in the far-field regime
Broader universality of rogue waves of infinite order
We show that the same special solution of the focusing nonlinear Schrödinger equation that has been shown to arise in a certain …
Deniz Bilman, Peter D. Miller
March, 2022 Physica D
PDF Cite DOI ArXiv
Far-field asymptotics for multiple-pole solitons in the large-order limit
The integrable focusing nonlinear Schrodinger equation admits soliton solutions whose associated spectral data consist of a single pair …
Deniz Bilman, Robert Buckingham, Deng-Shan Wang
January, 2021 Journal of Differential Equations
Cite DOI ArXiv
Far-field asymptotics for multiple-pole solitons in the large-order limit
On numerical inverse scattering for the Korteweg-de Vries equation with discontinuous step-like data
We present a method to compute dispersive shock wave solutions of the Korteweg–de Vries equation that emerge from initial data with …
Deniz Bilman, Thomas Trogdon
March, 2020 Nonlinearity
Cite DOI ArXiv
On numerical inverse scattering for the Korteweg-de Vries equation with discontinuous step-like data
Large-order asymptotics for multiple-pole solitons of the focusing nonlinear Schrödinger equation
We analyze the large-$n$ behavior of soliton solutions of the integrable focusing nonlinear Schrödinger equation with associated …
Deniz Bilman, Robert Buckingham
April, 2019 Journal of Nonlinear Science
Cite DOI ArXiv
Large-order asymptotics for multiple-pole solitons of the focusing nonlinear Schrödinger equation
Extreme superposition: Rogue waves of infinite order and the Painlevé-III hierarchy
We study the fundamental rogue wave solutions of the focusing nonlinear Schrödinger equation in the limit of large order. Using a …
Deniz Bilman, Liming Ling, Peter D. Miller
August, 2018 Duke Mathematical Journal
Cite Code DOI ArXiv
Extreme superposition: Rogue waves of infinite order and the Painlevé-III hierarchy
Benchmarking numerical methods for lattice equations with the Toda lattice
We compare the performance of well-known numerical time-stepping methods that are widely used to compute solutions of the …
Deniz Bilman, Thomas Trogdon
July, 2018 Applied Numerical Mathematics
Cite Code DOI ArXiv
A robust inverse scattering transform for the focusing nonlinear Schrödinger equation
We propose a modification of the standard inverse scattering transform for the focusing nonlinear Schrödinger equation (also other …
Deniz Bilman, Peter D. Miller
October, 2017 Communications on Pure and Applied Mathematics
Cite DOI ArXiv
A robust inverse scattering transform for the focusing nonlinear Schrödinger equation
Discrete integrable systems, Darboux transformations, and Yang–Baxter maps
This chapter is devoted to the integrability of discrete systems and their relation to the theory of Yang–Baxter (YB) maps. Lax pairs …
Deniz Bilman, ‪Sotiris Konstantinou-Rizos‬
July, 2017 CRM Series in Mathematical Physics
Cite DOI ArXiv
Numerical inverse scattering for the Toda lattice
We present a method to compute the inverse scattering transform (IST) for the famed Toda lattice by solving the associated …
Deniz Bilman, Thomas Trogdon
January, 2017 Communications in Mathematical Physics
Cite Code DOI ArXiv
Numerical inverse scattering for the Toda lattice
On the evolution of scattering data under perturbations of the Toda lattice
We present the results of an analytical and numerical study of the long-time behavior for certain Fermi–Pasta–Ulam (FPU) lattices …
Deniz Bilman, Irina Nenciu
September, 2016 Physica D
Cite DOI ArXiv

Posts

AMS Central Sectional Meeting to be held at UC in Spring 2023
After several postponements due to CoViD-19 pandemic, we are now on track to host a Central Sectional Meeting in April 2023. Stay tuned for the information on special sessions!
Deniz Bilman
May 4, 2022 1 min read at UC
AMS Central Sectional Meeting to be held at UC in Spring 2023
Taft Lecture by Percy Deift
Percy Deift, Silver Professor of Mathematics from the Courant Institute of Mathematical Sciences, New York University, will be giving the Taft Lecture in Spring 2020 at the University of Cincinnati. See the announcement. Mark your calendars for March 4, 2020, 4:00 PM! The lecture is in Room 500 Swift Hall.
Deniz Bilman
Dec 13, 2020 1 min read at UC
Taft Lecture by Percy Deift

Research cloud

Darboux transformations Deep Learning dispersive quantization dispersive shock waves Fermi-Pasta-Ulam-Tsingou lattices finite-gap solutions integrable systems inverse-scattering transform Korteweg-de Vries equation multiple-pole solitons nonlinear Schrödinger equation numerical inverse scattering Painlevé hierarchies perturbations of integrable systems Riemann-Hilbert problems rogue waves rogue waves of infinite order spectral singularities Toda lattice universality

Contact

  • bilman@uc.edu
  • 2815 Commons Way, Cincinnati, OH 45221
  • The building is French Hall West. My office is 5510 on the fifth floor.
  • No office hours during the summer.
  • Zoom me